If two identical spherical bodies of same material and dimensions are kept in contact, the gravitational…
If two identical spherical bodies of same material and dimensions are kept in contact, the gravitational force between them is proportional to $\mathrm{R}^{\mathrm{X}}$, where $\mathrm{x}$ is non zero integer
[Given : $\mathrm{R}$ is radius of each spherical body]
-4
4
2
-2
Solution
$\begin{aligned} F & =\frac{G \times m \times m}{(2 R)^2}=\frac{G \times\left(\frac{4}{3} \pi R^3 \rho\right)^2}{4 R^2} \\ & =\frac{4}{9} \pi^2 \rho^2 R^4 \\ \therefore \quad F & \propto R^4\end{aligned}$